CN106405536A - MIMO radar multi-target tracking resource management method - Google Patents

Abstract

The invention belongs to the technical field of MIMO radar, and particularly provides an MIMO radar multi-target tracking resource management method. Firstly traversal of controllable parameter combinations is performed, and whether the controllable parameter combinations can meet the detection probability and beam direction constraints is judged so as to form an MIMO radar control vector feasible set; then deviation cost and the energy resource consumption cost between the prediction tracking error covariance and the expected covariance of the targets are calculated under each control vector in the feasible set; and the two cost is integrated, and the optimal radar control vectors are acquired according to the criterion of the minimum integrated cost. The advantages that MIMO radar utilizes single beam to irradiate multiple targets can be fully exerted under the multi-target environment so that the sampling frequency of each target can be increased, the time resource utilization rate of radar can be effectively enhanced and the deviation between the actual tracking error covariance and the expected covariance of the targets can be reduced, and the tracking accuracy of the method can be controlled by the method through adjusting the expected tracking error covariance.

Description

A kind of MIMO radar multiple target tracking method for managing resource

Technical field

The invention belongs to MIMO radar technical field is and in particular to a kind of MIMO radar multiple target tracking resource management side Method.

Background technology

MIMO radar is a kind of widely studied at present and development new system radar.MIMO radar can be entered to array antenna The flexible Subarray partition of row is so as to both can launch the broad beam of low gain it is also possible to launch the narrow beam of high-gain, or is situated between In between the two, therefore in AF panel, target detection performance and target component, MIMO radar estimates that the aspects such as performance have ratio Other radar better performances.All kinds of resources for effective distribution MIMO radar are so that radar system resource and whole task are born Load matches, to give full play to radar performance it is necessary to implement effective management and running to MIMO radar.For MIMO radar Speech, the submatrix number of its flexibility and changeability makes radar emission wave beam more diversified, but also makes the resource management of MIMO radar simultaneously More complicated.

MIMO radar is followed the tracks of Resources Management and is referred to when carrying out target following, how effectively to distribute radar system Time-energy resource, is directed to working method, waveform selection, beam dispath and the Subarray partition of MIMO radar.Existing Radar tracking resource management's achievement in research has focused largely on control battle array radar.As document：“W.H.Gilson.Minimum power requirements for tracking[C].IEEE International Radar Conference,New York, 1990:In 417-421 ", W.H.Gilson has been on the premise of having taken into full account target maneuver characteristic, gives and under tracking mode is The functional relationship united between consumed minimum power and target tracking accuracy, tracking sampling cycle and signal to noise ratio.And for example literary composition Offer：“Krishnamurthy V,Evans R J.Hidden Markov model multiarm bandits:a methodology for beam scheduling in multitargettracking[J].IEEE Transactions on Signal Processing,2001,49(12):In 2893-2908 ", V.Krishnamurthy etc. is based on part observation Markov decision model proposes a kind of beam dispath method in multiple target tracking, and the method is by phased-array radar multiple target Tracing management problem is converted into a kind of hidden Markov Multiarm Bandit problem, proposes a kind of multiple target tracking with this Under resource allocation methods.And for example document：“T.Kirubarajan,Y.Bar-Shalom,W.D.Blair,et al.IMMPDF for radar management and tracking benchmark with ECM[J].IEEE Transactions on Aerospace and Electronic Systems,1998,34(4):In 1115-1134 ", Kirubarajan et al. have studied Resources Management during radar tracking under false-alarm and electronic interferences environment, the method using invariable false alerting is adaptively selected Detection threshold and radar waveform, that is, require echo signal to noise ratio to exceed certain thresholding, and echo signal to noise ratio be with the RCS of target, The distance amount relevant with transmitted waveform.And for example document：" Lu Jianbin, Xiao Hui, Xi Zemin, etc. phased-array radar wave beam waveform joint Self-adapting dispatching method [J]. system engineering and electronic technology, 2011,33 (1):Propose one kind in 84-88 " and be based on covariance The united beam waveform self-adapting dispatching method of control thought, the desired covariance to multiple goal settings, calculate current time The cost of tracing deviation and the cost of wave type energy, to determine the working method of next moment wave beam and the waveform selecting.And for example Document：" Zhang Zhenkai, Wang Fei, Zhou Jianjiang etc. auto-adaptive time scheduling of resource [J] in multiple target tracking. aviation journal, 2011,32 (3):A kind of auto-adaptive time resource regulating method based on IMMPDA method proposing in 522-530 ", first defines each The expectation tracking accuracy of target, with grey correlation theory design object function, with the sampling in particle swarm optimization solving model Cycle and residence time.All for phased-array radar in above method, configuration is optimized to different task parameters.

At present, follow the tracks of the research of resource management still in the starting stage for MIMO radar, achievement in research is less, and is mostly Tracking resource management under single goal scene；But because MIMO radar beam angle span scope is larger, single ripple can be passed through Bundle irradiates multiple targets simultaneously, more advantageous under multiple target tracking background.So the present invention proposes a kind of target-rich environment Lower MIMO radar follows the tracks of method for managing resource, the working method of joint MIMO radar, beam dispath, Subarray partition and waveform choosing Select the Time-energy resource to distribute radar system.Based on the thought of covariance control, consider the tracking accuracy of target with And radar resource consumption, minimized by making its integrate-cost, obtain optimum parameter sets.

Content of the invention

Object of the present invention is to provide a kind of MIMO radar multiple target tracking method for managing resource, the method is to each Target presets desired tracking accuracy, under conditions of the detection probability ensureing target and beam position meet the constraint, passes through So that the tracing deviation of target is minimized with the integrate-cost of resource consumption and obtain optimum scheduling parameter set, including the work of radar Make mode, waveform selection, beam position and submatrix number.

First the concept that the present invention commonly uses is explained：

MIMO radar working method：MIMO radar working method represents under normal circumstances, has in MIMO radar monitor area Multiple targets exist, and therefore MIMO radar must maintain the tracking to known target, i.e. MIMO thunder while finding fresh target The working method reaching at a time may be likely to as following the tracks of for search.And in the tracking mode, because MIMO radar is permissible Multiple targets are irradiated by single wave beam simultaneously, with the difference to target selection, the work of MIMO radar in the tracking mode Mode of making also is classified into multiple.For example：When current goal number is 2, MIMO radar working method is as follows：

Working method	0	1	2	3
					Implication	Search	Only follow the tracks of target 1	Only follow the tracks of target 2	Follow the tracks of target 1,2 simultaneously

When target number is D, the working method collection of MIMO radar is combined into：WhereinRepresent and appoint, from D target, all combinations taking 1 target, remaining is by that analogy.

The technical scheme is that：

A kind of MIMO radar multiple target tracking method for managing resource,

Assume that the current tracking moment is t_k, current target number of following the tracks of is D, t_kBefore moment, the filtering of all targets updates State is { t_k(i),X(t_k(i)),P(t_k(i)), wherein t_k(i)For the renewable time of i-th target, and t_k(i)≤t_k, i=1, 2,…,D；X(t_k(i)) it is i-th target in t_k(i)The state vector in moment, P (t_k(i)) it is i-th target in t_k(i)The shape in moment State error co-variance matrix.

Assume that the optional parameters collection of MIMO radar working method is combined into I_S, transmitted waveform optional parameters collection is combined into radar waveform The set of all transmitted waveforms composition in storehouse, it is designated as J, Subarray partition number optional parameters collection is combined into S；Assume t_kMoment radar Dominant vector ν (t_k) it is now desired to determine t_k+1The optimum control vector ν of moment MIMO radar_opt(t_k+1), method and step is as follows：

Step one：Traversal Subarray partition number optional parameters set, under each Subarray partition number parameter s, determines ripple Shu Zhixiang optional parameters set U_S；The optional parameters set U that radar beam points to_SFor：

When only comprising a target in wave beam, prediction beam position is u_pre, in interval [u_pre-0.5φ,u_pre+0.5 φ] in interval delta u travel through find optimum beam point to；When comprising target number in wave beam more than 1, each object beam is referred to To composite vector u_pre, in interval [minu_pre,maxu_pre] in interval delta u travel through find optimum beam point to；Wherein, φ is Half-power beam width,M is radar array element sum；

Step 2：Traversal controllable parameter { I_S,J,U_S, S } combination, the combination of every kind of controllable parameter forms radar control vector ν (t_k+1)=(I, j, u_s, s), I ∈ I_S, j ∈ J, u_s∈U_S, s ∈ S, travel through all dominant vectors and judge its whether meet the constraint：

Wherein, first constraint representation is in dominant vector ν (t_k+1) under the detection probability of target be higher than thresholding, P_d ^THRepresent The thresholding of target detection probability, P_d(ν(t_k+1)) represent dominant vector ν (t_k+1) under target detection probability；For example, when target When RCS obeys the distribution of Swerling I type, its detection probability is calculated as follows：

Wherein, P_faFor false-alarm probability, SNR (ν (t_k+1)) it is in dominant vector ν (t_k+1) under target signal to noise ratio：

Wherein, M is radar array number, P_tFor the total peak power of signal, η_eFor antenna effective area dutycycle,For t_kThe estimated value of the average RCS of moment target, λ is wavelength, τ^jFor the pulsewidth of waveform j, RⁱFor the radial distance away from radar for target i, N₀ For noise power spectral density, N₀=kT₀F₀, k is Boltzmann constant, T₀For radar receiver temperature, F₀Make an uproar for radar receiver Sonic system number, s is MIMO radar submatrix number,Gain pattern for radar：

Wherein, c₀=-2ln2, u_sPoint to for antenna beam, u_preFor the prediction beam position of target, φ is half-power beam Width.Second constraint representation requires target position in the half-power beam width of beam position；

Step 3：Dominant vector ν (t for meet the constraint formula (2)_k+1), calculate it in t_k+1When inscribe to each target Predicting tracing error covariance：

Wherein, Pⁱ(t_k+1|t_k,ν(t_k+1)) represent that when control vector be ν (t_k+1) when, the predicting tracing error association side of target i Difference；

IfRepresent t_k+1Moment will not be filtered to target i, then to its tracking error covarianceEnter Row prediction：

Wherein,For the sampling interval of target i, For the state-transition matrix of target i, Pⁱ (t_k(i)) it is target i in t_k(i)The estimation difference covariance matrix in moment,For the input distribution matrix of target i, Qⁱ (t_k(i)) for target i system mode noise covariance matrix；

If i is ∈ I, represent t_k+1Moment will be tracked to target i, then the estimation difference of the prediction of target i defences poor square jointly Battle array Pⁱ(ν(t_k+1)) be：

Wherein, K (ν (t_k+1)) it is in dominant vector ν (t_k+1) under kalman gain matrix：

Wherein, HⁱFor observing matrix, R (ν (t_k+1)) it is in dominant vector ν (t_k+1) under observation noise covariance matrix,

R(ν(t_k+1))=J diag (σ^r(ν(t_k+1))²,σ^b(ν(t_k+1))²,σ^e(ν(t_k+1))²)·J^T(10)

Wherein, the Jacobian transition matrix from spherical coordinate system to rectangular coordinate system, σ^r(ν(t_k+1)) it is in dominant vector ν (t_k+1) under radial distance measurement standard deviation, σ^b(ν(t_k+1)) it is in dominant vector ν (t_k+1) under azimuth determination standard deviation, σ^e(ν(t_k+1)) it is in dominant vector ν (t_k+1) under pitch angle measurement standard deviation, it is calculated as follows：

Wherein, Δ r (ν (t_k+1)) it is range resolution,WithFor beam angle, the typical case of constant c takes It is worth for 1.57；

Step 4：Dominant vector ν (t for meet the constraint formula (2)_k+1), calculate it in t_k+1When to inscribe tracking error inclined The integrate-cost value C (ν (t that difference is consumed with radar resource_k+1))：

Wherein,For the deviation cost of target following error and its expected value, it is calculated as follows：

D represents target number, the Diversity measure between f (A, B) representing matrix A and matrix B, desirable matrix 2-Norms, Row norm, row norm etc..E_jIt is operated in the resource consumption of waveform j；ψ{x_mIt is normalized function,

ψ{x_m}=x_m/max(x_m) (14)

α and β is respectively the weighted value after tracing deviation cost and resource consumption cost normalization, and alpha+beta=1；

Step 5：Determine t according to the minimum criterion of integrate-cost_k+1The dominant vector of moment MIMO radar：

Step 6：If I_opt=0, then in t_k+1Moment executes search mission；Otherwise utilize optimum waveform j_opt, optimum submatrix Number s_optAnd optimal beam sensingUpdate set I_optIn the state of target and estimate the average RCS of target；Assume mesh Target RCS σ (t_k) obedience average be σ_aveSwerling type distribution, that is,：

E{σ(t_k)=σ_ave(16)

t_k+1The target RCS value in momentCan be calculated according to radar equation, based on this observation, can be designed such as Under αfilter target RCS average is estimated：

In above formula,For t_k+1The Estimation of Mean of moment target RCS, α_tFor filter gain；

Step 7：Make k=k+1, return to step one, repeat above step until tracking process terminates.

The operation principle of the present invention is：

Under multiple target scene, MIMO radar, in each scheduling instance, is required for decision-making execution tracing task and is also carried out searching Rope task, and when executing tracing task, need to select target to be tracked from multiple targets, this correspond to MIMO thunder The working mode selection problem reaching；Meanwhile, MIMO radar typically has multiple work waves, adopts which kind of waveform when irradiating every time Correspond to the waveform selection problem of MIMO radar；Submatrix number due to MIMO radar can flexibly divide, and MIMO radar needs Decision-making is to be irradiated to multiple targets using single broad beam or be sequentially completed the irradiation to multiple targets using narrow beam, and this is right Answer the Subarray partition problem of MIMO radar；Additionally, determining that when being tracked being to target the beam position of radar is also The problem that MIMO radar needs to solve；So MIMO radar has in the controllable parameter of each scheduling instance：Working method, waveform selects Select, Subarray partition number, beam position.

Assume that the current tracking moment is t_k, current target number of following the tracks of is D, t_kBefore moment, the filtering of all targets updates State is { t_k(i),X(t_k(i)),P(t_k(i)), wherein t_k(i)For the renewable time of i-th target, and t_k(i)≤t_k, i=1, 2,…,D；X(t_k(i)) it is i-th target in t_k(i)The state vector in moment, P (t_k(i)) it is i-th target in t_k(i)The shape in moment State error co-variance matrix.Assume that the optional parameters collection of MIMO radar working method is combined into I_S, transmitted waveform optional parameters set For J, beam position optional parameters collection is combined into U_S, Subarray partition number optional parameters collection is combined into S；Assume t_kThe control of moment radar Vectorial ν (t_k) it is now desired to determine t_k+1The optimum control vector of moment MIMO radar I_opt∈I_S, j_opt∈ J,s_opt∈S.

When MIMO radar is tracked to target, it is higher than certain door that selected dominant vector must make target detection probability Limit；Simultaneously need to constrain it is desirable to target position is in the half-power beam width of beam position further to beam position, Shown in two constraints such as formulas (2).

In the tracking to target for the MIMO radar, it is generally desirable to adjust the tracking accuracy of target, using covariance Control technology can effectively be controlled to target tracking accuracy.So-called covariance control technology is it is simply that pre- to each target First set a desired tracking accuracy, that is, expect covariance matrix, the controllable parameter then adjusting radar is in certain tolerance and standard The actual covariance of target is then made down to approach its expected value.On the other hand, target tracking accuracy is higher often means that radar The system resource consuming is higher, and the lifting of the such as raising of tracking sampling rate and accuracy of waveform can improve the tracking essence of target Spend but the time resource of radar and the consumption of energy resource can be increased simultaneously.So need comprehensive in the controllable parameter of decision-making radar Close the resource consumption of covariance control effect and radar when considering target following.

t_k+1When, inscribe shown in the integrate-cost such as formula (12) that MIMO radar tracking error deviation is consumed with energy resource, formula InRepresent and controlling vector ν (t_k+1) under target prediction estimation difference covarianceWith Expect covarianceDiversity factor；Selection for F [] can have covariance deviation average and maximum two kinds of covariance deviation Criterion, is designated as F-1 criterion and F-2 criterion, the expression formula of F [] is respectively under both criterions respectively：

F-1 criterion：

F-2 criterion：

Wherein what function f (A, B) represented is the Diversity measure between matrix A and matrix B, and it can select group as needed Multiple different concrete representations, such as conventional matrix 2-Norms, row norm, row norm, Frobenius norm, matrix Mark and matrix singular value decomposition etc.；In formula (12), E_jFor being operated in the resource consumption of waveform j, here shown as radar wave The mean power of shape；Due to tracking error covariance deviation and waveform power be in cost function two diverse because Element, dimension also differs it is impossible to directly be weighted suing for peace to it, so design normalized function ψ { x_m}=x_m/max(x_m) right All independent variables to maximum max (x_m) be normalized；Then MIMO radar follow the tracks of method for managing resource control to Measuring optimal scheduling model is：

According to t_k+1The principle of the total Least-cost of moment MIMO radar, can obtain the optimal control inputs of MIMO radar, such as Shown in formula (15)；In formula (20), the predicting tracing error covariance of targetCalculating such as formula (6)-(10) shown in； Detection probability P_d(ν(t_k+1)) calculating such as formula (3) shown in.

In sum, the present invention provides MIMO radar under a kind of target-rich environment to follow the tracks of method for managing resource, according to tracking The criterion of the integrate-cost value that error deviation is consumed with radar resource, each moment is selected to the working method of MIMO radar, waveform Select, beam position and Subarray partition carry out optimum allocation.Controllable parameter combination is carried out time by method proposed by the present invention first Go through, judge whether it can meet the constraint of detection probability and beam position, thus forming MIMO radar dominant vector feasible set；Connect Get off under each dominant vector in feasible set, calculate inclined between the predicting tracing error covariance of target and expectation covariance Difference cost and energy resource consume cost；Comprehensive two kinds of costs, obtain optimum radar control according to the minimum criterion of integrate-cost Vector.Under target-rich environment, the method can give full play to the advantage that MIMO radar utilizes the multiple target of single beam, Increase the sampling number to each target, effectively improve the time resource utilization rate of radar and reduce the actual tracking error association of target Deviation between variance and expectation covariance, and the method can be by adjusting desired tracking error covariance come controlling party The tracking accuracy of method.

Brief description

Fig. 1 is the real motion track of target.

Fig. 2 is the actual filtering error covariance on X-direction position.

Fig. 3 is the actual filtering error covariance on Y-direction position.

Fig. 4 is MIMO radar working method.

Fig. 5 numbers for MIMO radar waveform.

Fig. 6 points to for MIMO radar wave beam.

Fig. 7 is MIMO radar Subarray partition number.

Specific embodiment

With reference to the accompanying drawings and examples the present invention is described in further details.

Based on detailed technology scheme of the present invention, obtain the optimal control inputs of MIMO radar, same scene in each moment Under, by the contrast with phased-array radar, to represent the effect of the present invention.

It is assumed that the running parameter of radar is as shown in the table,

Table 1 radar running parameter

Assume two targets planar moving with uniform velocity of radar tracking, the movement time of target 1 is 0-100s, initially Position is [122,122] km, and speed is [45,50] m/s；The movement time of target 2 be 20-100s, initial position be [123, 124] km, speed is [70,0] m/s.Two targets movement locus as shown in Figure 1.The process noise auto-correlation of two targets Matrix is：

Two targets are Swerling I type distribution objectives, and its RCS average is 1m².

The optional parameters set I of MIMO radar working method_S={ 0,1,2,3 }, working method 0 represents that MIMO radar is in Way of search, working method 1 represents that MIMO radar is tracked to target 1, and working method 2 represents that MIMO radar is entered to target 2 Line trace, working method 3 represents and target 1,2 is tracked simultaneously.

MIMO radar transmitted waveform optional parameters is as shown in the table, wherein τ_eFor pulse width, τ_sFor pulse compression width, Δ r is range resolution ratio, and E is the emitted energy of every kind of waveform.Wherein waveform number be 7 waveform be acquisition waveforms.

Table 2 radar emission waveform parameter

In simulations, the optional parameters set U that radar beam points to_SDiscrete interval be Δ u=0.002rad.

The optional parameters collection of radar Subarray partition number is combined into：

S={ 1,2,4,8,16,32,64,128,256,512,1024,2048 } (22)

The detection probability thresholding of target is set to 0.95, and false-alarm probability is 10^-6, MIMO radar executes searches for or tracing task Be spaced apart 0.1s, in cost function, the cost of covariance deviation and energy expenditure is respectively α=0.9, β=0.1.For cost Matrix measures in functionHere only consider the tracking error covariance deviation on X and Y-direction position.

Wherein,Representing matrixElement on (1,1) position, remaining is similar to.Target 1 and target 2 are in X and Y-direction Expectation tracking error variance on position is 30m.

Draw target 1 and actual filtering error variance change curve on X and Y-direction position for the target 2, P₁₁And P₃₃Point Not Biao Shi target following when variance on X-direction and Y-direction position, as shown in Figure 2 and Figure 3.It can be seen that this The method of bright proposition can efficiently control the tracking accuracy of target, and target 1 is substantially all with the tracking covariance control of target 2 Reach expected requirement.

Draw the dominant vector change curve of MIMO radar under single Monte Carlo.Fig. 4 gives method to MIMO radar The control result of working method, in figure Y-axis ' 0 ' represents execution search mission, and ' 1 ' represents the tracking to target 1 for the execution, ' 2 ' Represent the tracking to target 2 for the execution, ' 3 ' execute the tracking to target 1 and target 2 simultaneously.It can be seen that MIMO radar The tracking simultaneously to two targets can be realized.

The result that Fig. 5 selects to MIMO radar waveform for method, in figure Y-axis ' 1-6 ' represent 6 kinds of waveforms of radar, ' 7 ' Represent acquisition waveforms.It can be seen that being gradually increased with target and radar radial distance, MIMO radar is selected Accuracy of waveform assumes the trend being gradually increased.

The result that Fig. 6 dispatches to beam position for method, in figure point represents the beam position of target 1 ,+expression a target 2 beam position, point with+overlap and represent that this wave beam is tracked to two targets simultaneously.

The result that Fig. 7 selects to Subarray partition number for method.

In order to show that the present invention proposes the performance of method further, by method proposed by the present invention and phased-array radar with Track performance is contrasted, and simulating scenes parameter setting is identical with MIMO radar, and difference is that phased-array radar submatrix number is fixed For 1, each of which moment is only tracked to a target, and beam position is the prediction beam position of target.

In terms of following four, it is estimated：To the control of tracking accuracy, system capacity resource consumption, tracing deviation With the integrate-cost of resource consumption and to system time resource utilization.Adopt following four index successively：

Each target average covariance controls wow and flutter：

Wherein, N is Monte Carlo number of times, K_nFor executing the scheduling times of tracing task in n-th Monte Carlo,For n-th K-th sampling instant in secondary Monte Carlo,ForThe covariance control wow and flutter in moment, it is calculated as follows：

ForThe target number that moment updates,ForThe covariance matrix in moment, f () is selected Certain matrix measures,Represent the expectation covariance matrix of i-th target.

Average tracking power：

Wherein,ForThe power of moment transmitted waveform,ForThe pulse width of moment transmitted waveform, φ can With equivalent be seen as radar to target following when the mean power that consumed.

Average cost：

Wherein,ForThe value of moment object function.

With respect to phased-array radar, the degree of improvement to time resource utilization rate for the MIMO：

Define system time resource utilization first：

N_sFor the total scheduling times of system in a Monte Carlo,ForThe target number that moment updates, works as system During execution search mission, orderD is total target number.For phased-array radar, because each of which moment can only be right One target is tracked, and its system time resource utilization isAnd MIMO radar can multiple targets be carried out simultaneously with Track, its system time resource utilization is higher than phased array, with respect to phased array, calculates MIMO radar to time resource utilization rate Degree of improvement.

Wherein, η_PFor the time resource utilization rate of phased-array radar, η_MTime resource utilization rate for MIMO radar.

Under different cost function coefficients, it is right that the tracking performance of method proposed by the present invention and phased-array radar is carried out Table 3 is performance comparison result to ratio.

Table 3 MIMO radar and the performance comparison result of phased-array radar

As can be seen from the above table, under different cost coefficients, the covariance control wow and flutter of MIMO radar is respectively less than phase Control battle array radar, illustrates that method proposed by the present invention is better than phased-array radar in the control to the tracking accuracy of target.Relatively MIMO radar and the average tracking power of phased-array radar, when cost coefficient is more focused on covariance deviation, phased-array radar Energy resource consume less；And cost coefficient is when being 0.5,0.5, the energy resource of MIMO radar consumes less；When cost system When number is more focused on energy resource consumption, the energy resource consumption of two kinds of radars is of substantially equal.Under different cost coefficients, The average cost of MIMO radar is respectively less than phased-array radar, illustrates when considering error of covariance with energy resource consumption, Method performance proposed by the present invention is more excellent.Under three kinds of different objective function coefhcients, MIMO radar compared with phased-array radar when Between utilization rate all have improvement.When cost coefficient is more focused on covariance deviation, MIMO radar changes to time resource utilization rate Kind degree becomes apparent from.In sum, method proposed by the present invention can be entered to the tracking accuracy of all targets under target-rich environment Row efficiently controls.Compared to the tracking of phased-array radar, method proposed by the present invention is in the control of the tracking accuracy to target On, and it is better than phased-array radar on the integrate-cost of covariance control and energy resource consumption.And method proposed by the present invention The time resource utilization rate of radar can be effectively improved.

The above, the only specific embodiment of the present invention, any feature disclosed in this specification, except non-specifically Narration, all can be replaced by other alternative features that are equivalent or having similar purpose；Disclosed all features or all sides Method or during step, in addition to mutually exclusive feature and/or step, all can be combined in any way.

Claims (1)

1. a kind of MIMO radar multiple target tracking method for managing resource, comprises the following steps：

The current tracking moment is t_k, current target number of following the tracks of is D, t_kBefore moment, the filtering of all targets more new state is {t_k(i),X(t_k(i)),P(t_k(i)), wherein t_k(i)For the renewable time of i-th target, and t_k(i)≤t_k, i=1,2 ..., D；X (t_k(i)) it is i-th target in t_k(i)The state vector in moment, P (t_k(i)) it is i-th target in t_k(i)The state error association in moment Variance matrix；

The optional parameters collection of setting mimo Radar operation modes is combined into I_S, transmitted waveform optional parameters collection is combined in radar waveform storehouse The set of all transmitted waveform compositions, is designated as J, Subarray partition number optional parameters collection is combined into S；t_kThe dominant vector of moment radar ν(t_k) it is now desired to solve t_k+1The optimum control vector ν of moment MIMO radar_opt(t_k+1)；

Step one：Traversal Subarray partition number optional parameters set, under each Subarray partition number parameter s, determines that wave beam refers to To optional parameters set U_S, the optional parameters set U that radar beam points to_SFor：

When only comprising a target in wave beam, prediction beam position is u_pre, in interval [u_pre-0.5φ,u_pre+ 0.5 φ] in Traveled through with interval delta u and find optimum beam sensing；When comprising target number in wave beam more than 1, each object beam is pointed to and closes Become vectorial u_pre, in interval [minu_pre,max u_pre] in interval delta u travel through find optimum beam point to；Wherein, φ is half work( Rate beam angle,M is radar array element sum；

Step 2：Traversal controllable parameter { I_S,J,U_S, S } combination, the combination of every kind of controllable parameter forms radar control vector ν (t_k+1)=(I, j, u_s, s), I ∈ I_S, j ∈ J, u_s∈U_S, s ∈ S, travel through all dominant vectors and judge its whether meet the constraint：

$\left\{\begin{array}{c}{P}_d\left(v\right(t_{k+1}\left)\right)\&GreaterEqual;{P_d}^H\\ u-0.5\mathrm{\&phi;}<u_s<u+0.5\mathrm{\&phi;}\end{array}\right.$

Wherein, first constraint representation is in dominant vector ν (t_k+1) under the detection probability of target be higher than thresholding, P_d ^THRepresent target The thresholding of detection probability, P_d(ν(t_k+1)) represent dominant vector ν (t_k+1) under target detection probability；The RCS of target setting obeys Swerling I type is distributed, and its detection probability is calculated as follows：

$P_d\left(v\right(t_{k+1}\left)\right)={P_{fa}}^{1/(1+SNR(v\left(t_{k+1}\right)\left)\right)}$

Wherein, P_faFor false-alarm probability, SNR (ν (t_k+1)) it is in dominant vector ν (t_k+1) under target signal to noise ratio：

$SNR\left(v\right(t_{k+1}\left)\right)=\frac{M^3{P}_t{\left({\mathrm{\&pi;\&eta;}}_e\right)}^2{\widehat{\mathrm{\&sigma;}}}_{ave}\left(t_k\right){\mathrm{\&lambda;}}^2{\mathrm{\&tau;}}^j{G_{t0}}^{u_s,s}}{{\left(4\mathrm{\&pi;}\right)}^3{\left(R^i\right)}^4{N}_{0}s}$

Wherein, M is radar array number, P_tFor the total peak power of signal, η_eFor antenna effective area dutycycle,For t_kWhen Carve the estimated value of the average RCS of target, λ is wavelength, τ^jFor the pulsewidth of waveform j, RⁱFor the radial distance away from radar for target i, N₀For making an uproar Power sound spectrum density, N₀=kT₀F₀, k is Boltzmann constant, T₀For radar receiver temperature, F₀For noise of radar receiver system Number, s is MIMO radar submatrix number,Gain pattern for radar：

${G_{t0}}^{u_s,s}={\&lsqb;\exp \left(c_0\frac{{(u_{pre}-u_s)}^2}{{\mathrm{\&phi;}}^2}\right)\&rsqb;}^2$

Wherein c₀=-2ln2, u_sPoint to for antenna beam, u_preFor the prediction beam position of target, φ is half-power beam width；

Second constraint representation requires target position in the half-power beam width of beam position；

Step 3：Dominant vector ν (t for meet the constraint formula_k+1), calculate it in t_k+1When inscribe predicting tracing to each target Error covariance：

$P^i\left(t_{k+1}\right|t_k,v\left(t_{k+1}\right))=\left\{\begin{array}{c}{P}^i\left(t_{k+1}^{-}\right),i\&NotElement;I\\ P^i\left(v\right(t_{k+1}\left)\right),i\&Element;I\end{array}\right.$

Wherein, Pⁱ(t_k+1|t_k,ν(t_k+1)) represent that when control vector be ν (t_k+1) when, the predicting tracing error covariance of target i；

IfThen to its tracking error covarianceIt is predicted：

$P^i\left(t_{k+1}^{-}\right)=F^i\left(T_k^i\right)P^i\left(t_{k\left(i\right)}\right)F^{iT}\left(T_k^i\right)+G^i\left(T_k^i\right)Q^i\left(t_{k\left(i\right)}\right)G^{iT}\left(T_k^i\right)$

Wherein,Sampling interval for target i： For the state-transition matrix of target i,For Target i is in t_k(i)The estimation difference covariance matrix in moment,For the input distribution matrix of target i,For target The system mode noise covariance matrix of i；

If i is ∈ I, the estimation difference covariance matrix P of the prediction of target iⁱ(ν(t_k+1)) be：

$P^i\left(v\right(t_{k+1}\left)\right)=\&lsqb;I_n-p_d\left(v\right(t_{k+1}\left)\right)K\left(v\right(t_{k+1}\left)\right)H^i\&rsqb;P^i\left(t_{k+1}^{-}\right)$

Wherein, K (ν (t_k+1)) it is in dominant vector ν (t_k+1) under kalman gain matrix：

$K\left(v\right(t_{k+1}\left)\right)=P^i\left(t_{k+1}^{-}\right)H^{iT}{\{H^i{P}^i\left(t_{k+1}^{-}\right)H^{iT}+R\left(v\right(t_{k+1}\left)\right)\}}^{-1}$

Wherein, HⁱFor observing matrix, R (ν (t_k+1)) it is in dominant vector ν (t_k+1) under observation noise covariance matrix：

R(ν(t_k+1))=J diag (σ^r(ν(t_k+1))²,σ^b(ν(t_k+1))²,σ^e(ν(t_k+1))²)·J^T

Wherein, the Jacobian transition matrix from spherical coordinate system to rectangular coordinate system, σ^r(ν(t_k+1)) it is in dominant vector ν (t_k+1) The standard deviation of lower radial distance measurement, σ^b(ν(t_k+1)) it is in dominant vector ν (t_k+1) under azimuth determination standard deviation, σ^e(ν (t_k+1)) it is in dominant vector ν (t_k+1) under pitch angle measurement standard deviation, it is calculated as follows：

${\mathrm{\&sigma;}}^r\left(v\right(t_{k+1}\left)\right)=\frac{\mathrm{\&Delta;}r\left(v\right(t_{k+1}\left)\right)}{\sqrt{12}}$

${\mathrm{\&sigma;}}^b\left(v\right(t_{k+1}\left)\right)=\frac{B_w^b\left(t_{k+1}\right)}{(c\&CenterDot;\sqrt{2SNR\left(v\left(t_{k+1}\right)\right)})}$

${\mathrm{\&sigma;}}^e\left(v\right(t_{k+1}\left)\right)=\frac{B_w^e\left(t_{k+1}\right)}{(c\&CenterDot;\sqrt{2SNR\left(v\left(t_{k+1}\right)\right)})}$

Wherein, Δ r (ν (t_k+1)) it is range resolution,WithFor the beam angle of radar antenna, constant c's Typical value is 1.57；

Step 4：Dominant vector ν (t for meet the constraint formula_k+1), calculate it in t_k+1When inscribe tracking error deviation and radar The integrate-cost value C (ν (t of resource consumption_k+1))：

$C\left(v\right(t_{k+1}\left)\right)=\mathrm{\&alpha;}\mathrm{\&psi;}\{F\&lsqb;{\stackrel{\&RightArrow;}{P}}_0,\stackrel{\&RightArrow;}{P}\left(v\right(t_{k+1}\left)\right)\&rsqb;\}+\mathrm{\&beta;}\mathrm{\&psi;}\left\{E_j\right\}$

Wherein,For the deviation cost of target following error and its expected value, it is calculated as follows：

$F({\stackrel{\&RightArrow;}{P}}_0,\stackrel{\&RightArrow;}{P})=\underset{i=1}{\overset{D}{\&Sigma;}}f(P_o^i,P^i)/D$

D represents target number, the Diversity measure between f (A, B) representing matrix A and matrix B, E_jThe resource being operated in waveform j disappears Consumption, ψ { x_mIt is normalized function：ψ{x_m}=x_m/max(x_m)；

α and β is respectively weighted value and alpha+beta=1 after tracing deviation cost and resource consumption cost normalization；

Step 5：Determine t according to the minimum criterion of integrate-cost_k+1The dominant vector of moment MIMO radar：

$v_{opt}\left(t_{k+1}\right)=(I_{opt},j_{opt},u_{s_{opt}},s_{opt})=\arg \min C\left(v\right(t_{k+1}\left)\right)$

Step 6：If I_opt=0, then in t_k+1Moment executes search mission；Otherwise utilize optimum waveform j_opt, optimum submatrix number s_optAnd optimal beam sensingUpdate set I_optIn the state of target and estimate the average RCS of target；Target setting RCSσ(t_k) obedience average be σ_aveSwerling type distribution, that is,：

E{σ(t_k)=σ_ave

t_k+1The target RCS value in momentCan be calculated according to radar equation, based on this observation, be designed following α filter Ripple device is estimated to target RCS average：

${\widehat{\mathrm{\&sigma;}}}_{ave}\left(t_{k+1}\right)={\widehat{\mathrm{\&sigma;}}}_{ave}\left(t_k\right)+{\mathrm{\&alpha;}}_t\left(\widehat{\mathrm{\&sigma;}}\right(t_{k+1})-{\widehat{\mathrm{\&sigma;}}}_{ave}(t_k\left)\right)$

Wherein,For t_k+1The Estimation of Mean of moment target RCS, α_tFor filter gain；

Step 7：Make k=k+1, return to step one, repeat above step until tracking process terminates.